Hamas' spokesman Abdullatif al-Qanu stressed that the group's decision to join the "right to return" march showed the Hamas' alignment with Palestinian people.
Two farmers have also been killed in proximity to the fence since 2014 and at least 26 have been injured, excluding the over 155 killed and 17,000 injured by Israeli gunfire along the border fence in the March of Return demonstrations that started on March 30.
They also demand an end to Israel's 11-year blockade of the Gaza Strip, which has gutted the coastal enclave's economy and deprived its roughly 2 million inhabitants of many basic commodities.
The vessel was taken to the Israeli port of Ashdod, while the crew were detained for "further enquiry". Several of the exiled leaders attended the border protests Friday.
The Israeli military said troops had responded with "riot dispersal means" and had operated "according to standard operating procedures", a term that refers to the use of accurate live fire, after some Gazans broke through the border fence and attacked troops with firebombs and an explosive device.
It said a tank struck a Hamas post in response.
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Worldwide experts and aid organizations including the United Nations have repeatedly called the Israeli policy a collective punishment against Gazans for what Israel perceives as a threat by the Islamic Resistance group Hamas.
With borders to both Egypt and Israel largely sealed in recent years, Gaza suffers from desperately high rates of poverty and unemployment.
Earlier this week the Israeli navy intercepted a Norwegian-flagged activist boat, one of four that left Scandinavia in mid-May.
"The ship was monitored and was intercepted in accordance with worldwide law", the Israeli military claimed.
The Israel Navy seized a ship overnight Friday sailing from Europe in an attempt to break the naval blockade on the Gaza Strip, the military said.
Similar attempts by activists to challenge the Israeli naval blockade of Gaza have been foiled before.